angular momentum - Law of the lever - Explained Physically

Thanks for reading.

I've seen the "Archimedes Proof" of the law of the lever, and many similar ones, but...at the end of the day, all they're doing is getting observations about the way rotating bodies behave, and using those observations as axioms.

By defining torque to be the cross product of force and distance, we're just creating new terminology, but we aren't really explaining physically why it is that a force applied at a greater distance would be better at spinning something than a force applied at a lesser distance.

For example, say the green man and the pink man weigh exactly the same, but the green man is half as far from the pivot point as the pink man is. The rod will rotate towards the pink man.

Why?

I think that the reason that the green man doesn't have as much "spinning" power as the pink man does must have to do with the molecules of the bar. In a sense, the pink man will cause more bending in the bar, and it'll want to straighten out towards his direction (forgive me if that doesn't make any sense, it's just a thought).

Can someone please explain, from the approach of the atomic interactions in the rigid body connecting both the pink man and the green man to the fulcrum, and without using the concept of torque, why it is that the bar rotates towards the pink man?

And, if the torque equation could then be derived from that physical explanation, that would be awesome!

In summary, I'd like to know how to approach the concept of torque with atomic theory. I'd like to understand the interatomic electromagnetic forces in a rigid rod, how momentum travels along a rigid rod when we apply forces perpendicular to its length, and how that leads to the force being "amplified" by larger distances from the pivot point

Thanks!